function [x] = var_decode(x_norm, bounds)
% VAR_DECODE - Decodes the normalized variables x_norm into a normal float representation
% 
% Inputs: 
%   x_norm = [ number_of_samples x N_var ] input matrix of normalized variables to be decoded
%   bounds = [ number_of_variables x 2 ] input matrix where the ith row is the valid bounds for the ith variable
%   
% Outputs:
%   x = [ number_of_samples x N_var ] unnormalized encoding of each variable
% 
% Written by:
% -- 
% John L. Weatherwax                2006-08-28
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% Check inputs:
assert( size(bounds,2)==2, 'bounds input must have two columns' );
N_var     = size(bounds,1);
N_samples = size(x_norm,1);

% Compute the decoded variables:
% 
x_low  = repmat( bounds(:,1), [1,N_samples] ).';
x_len  = repmat( bounds(:,2) - bounds(:,1), [1,N_samples] ).';

x = x_norm .* x_len + x_low;